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# Recent problems solved by 'stanbon'

Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 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 Travel_Word_Problems/147411: An airplane flew for 6 hours with a tail of 60 km/hr. The return flight against the same wind took 8 hours. Find the speed of the airplane in still air.1 solutions Answer 107797 by stanbon(57984)   on 2008-07-07 07:17:32 (Show Source): You can put this solution on YOUR website!An airplane flew for 6 hours with a tail of 60 km/hr. The return flight against the same wind took 8 hours. Find the speed of the airplane in still air. ----------- With the wind DATA: Time = 6 hrs ; rate = p+60 mph ; distance = tr = 6(p+60) = 6p+360 miles --------- Against the wind DATA: Time = 8hrs ; rate = p-60 mph ; distance = tr = 8(p-60) = 8p-480 miles --------- EQUATION: distance with = distance against 6p+360 = 8p-480 2p = 840 p = 480 mph (speed of the plane in still air) =========== Cheers, Stan H.
 absolute-value/147423: evaluate the numerical expression 1) 5[(12)+60]/101 solutions Answer 107796 by stanbon(57984)   on 2008-07-07 07:13:09 (Show Source): You can put this solution on YOUR website!evaluate the numerical expression 1) 5[(12)+60]/10 -------- = 5[72]/10 = 72/2 = 36 ========== Cheers, Stan H.
 Age_Word_Problems/147425: Mr.Reyes is 20 years older than his son, how old are the father and the son if Mr. Reyes is a 6 times as old as his son?1 solutions Answer 107795 by stanbon(57984)   on 2008-07-07 07:11:16 (Show Source): You can put this solution on YOUR website!Mr.Reyes is 20 years older than his son, R = s + 20 ------------- how old are the father and the son if Mr. Reyes is a 6 times as old as his son? R = 6s ------------- Solve by substitution: 6s = s+20 5s = 20 s = 4 yrs old (Son's age) R = s+20 = 4+20 = 24 yrs old (Mr. Reyes age) ================ Cheers, Stan H.
 absolute-value/147402: I tried to submit this earlier but it does not seem to have gone through. Please help a Mom with another absolute value question. Please provide solution with explanation so that I can help my child. Find the absolute value inequality: [2, 10]1 solutions Answer 107777 by stanbon(57984)   on 2008-07-06 22:30:21 (Show Source): You can put this solution on YOUR website!I tried to submit this earlier but it does not seem to have gone through. Please help a Mom with another absolute value question. Please provide solution with explanation so that I can help my child. Find the absolute value inequality: [2, 10] ----------- The middle point is 6. The distance from the middle to either end point is 4. ------------- Absolute value inequality: |x-6|<= 4 ================= Cheers, Stan H.
 Graphs/147365: graph the system of inequalities. y is greater than or equal to -3 x is greater than or equal to 41 solutions Answer 107776 by stanbon(57984)   on 2008-07-06 21:59:57 (Show Source): You can put this solution on YOUR website!graph the system of inequalities. y is greater than or equal to -3 Draw a line thru all points where y = -3. Shade the half-plane above the line. ------------------------ x is greater than or equal to 4 Draw a vertical line thru all points where x = 4. Shade the half-plane to the right of x = 4. -------------------- The solution is the intersection of the half-planes including the boundary of the intersection. =================== Cheers, Stan H.
 Travel_Word_Problems/147399: The current was 3 mph. The fast boat could go 92 miles downstream in the same time it took to go 68 miles upstream. How lond did each trip take and what was the speed of the boat in still water?1 solutions Answer 107774 by stanbon(57984)   on 2008-07-06 21:54:32 (Show Source): You can put this solution on YOUR website!The current was 3 mph. The fast boat could go 92 miles downstream in the same time it took to go 68 miles upstream. How lond did each trip take and what was the speed of the boat in still water? ------------------------ Let the boat speed in still water be "b". ---------- Downstream DATA: distance = 92 miles ; rate = b+3 mph ; time = d/r = 92/(b+3) hrs. ----------------- Upstream DATA: disance = 68 miles ; rate = b-3 mph ; time = d/r = 68/(b-3) hrs. ----------------- EQUATION: time up = time down 68/(b-3) = 92/(b+3) 68b+204 = 92b-276 24b = 480 b = 20 mph (speed of the boat in still water) ============= Cheers, Stan H.
 Radicals/147401: State the domain of l(x)=5x-4 what is the case here??1 solutions Answer 107773 by stanbon(57984)   on 2008-07-06 21:48:48 (Show Source): You can put this solution on YOUR website!State the domain of l(x)=5x-4 what is the case here?? ------------------------ Domain: All Real Numbers ---------------- What do you mean by case? Cheers, Stan H.
 Functions/147397: If I am at the gas station filling my tank with gas. The function C(g) represents the cost C of filling up the gas tank with g gallons. Given the equation, what does the number 3.03 represent? What would C(2) or C(9) be? If I graph C(g), what would be an appropriate domain and range be? 1 solutions Answer 107770 by stanbon(57984)   on 2008-07-06 20:59:53 (Show Source): You can put this solution on YOUR website! C(g)=3.03(g) If I am at the gas station filling my tank with gas. The function C(g) represents the cost C of filling up the gas tank with g gallons. Given the equation, what does the number 3.03 represent? What would C(2) or C(9) be? --------------------- 3.03 is the slope of the equation and is the increased price of the cost (C) for each additional gallon of gas. ---------- C(2) = 3.03*2 = \$6.06 ------- C(9) = 3.03*9 = \$27.27 -------- Cheers, Stan H.
 Polynomials-and-rational-expressions/147370: 1. Find (f-g)(x) if f(x)=x^2-2x-24 and g(x)=x^2-x-30; 2. If f(x)=x+4 and g(x)=2x^2-x-1, find the composition(fog)(2); 3. Write the sentence as an equation: y varies directly as x; 4. Use the compound interest formula a=p(1+r/n)^nt, to find A when investing a principle of \$500.00 at an interest rate of 5% for 10 years, compounded quarterly. Thank you1 solutions Answer 107769 by stanbon(57984)   on 2008-07-06 20:58:32 (Show Source): You can put this solution on YOUR website!1. Find (f-g)(x) if f(x)=x^2-2x-24 and g(x)=x^2-x-30; (f-g)(x) = f(x)-g(x) = x^2-2x-24 - (x^2-x-30) = -x + 6 --------------------- 2. If f(x)=x+4 and g(x)=2x^2-x-1, find the composition(fog)(2); (fog)(2) = f[g(2)] = f[2*2^2-2-1] = f[5] = 5+4 = 9 -------------- 3. Write the sentence as an equation: y varies directly as x; y = kx -------------- 4. Use the compound interest formula a=p(1+r/n)^nt, to find A when investing a principle of \$500.00 at an interest rate of 5% for 10 years, compounded quarterly. A(10) = 500(1+(0.05/4))^(4*10) A(10) = 500(1.0125)^(40) A(10) = 500*1.643619... A(10) = \$821.81 ============= Cheers, Stan H.
 Exponents/147396: Please help me to simply this 1 solutions Answer 107768 by stanbon(57984)   on 2008-07-06 20:23:07 (Show Source): You can put this solution on YOUR website!Please help me to simply this 9^(3/2) ----------- The "2" in the exponent means "take the square root". ------------ The "3" in the exponent means "cube" -------------- 1st take the square root of 9 to get: = 3 ^3 --------- Now cube the three ---------- = 27 ============ Cheers, Stan H.
 Probability-and-statistics/147394: How do you calculate P value of Z from the chart?1 solutions Answer 107767 by stanbon(57984)   on 2008-07-06 20:19:51 (Show Source): You can put this solution on YOUR website!If the test is 2-tail, the p-value for a particular z test statistic is two times the probability that z is greater than the test statistic value if the test statistic value is positive, or that z is less than the tst statistic value if the test statistic is negative. ------------ If the test is right-tailed, the p-value for a particular z test statistic is the probability that z is greater than the test statistic value. -------------- If the test is left-tailed, the p-value for a particular z test statistic is the probability that z is less than the test statistic value. ================ Cheers, Stan H.
 Linear-systems/147364: Hi, I dont know what Im doing wrong I need help please. Here is the question: One year ago you invested \$4300 into three accounts that earn 3.25%, 4%, and 5.75% annual interest. The interest you earned after one year is \$193. You remembered you invested three times as much in the 4% account than you did the 3.25% account. How much did you invest in each type of account? This is what i have so far, I dont think its right. x + y + Z = 4300 325x + 400Y + 575z = 19300 Y=3x x + (3x) + Z = 4300 4x + z = 4300 325x + 400 (3x) + z =19300 1525x +575z = 19300 (-575) 4x + z = 4300 (-575) -2300x - 575z =-2472500 1525x + 575z = 19300 -775x = -2453200 x=3165.4 then when I do 3 times x to get y it doesnt fit with the total of 4300. I dont know please help me thank you.1 solutions Answer 107766 by stanbon(57984)   on 2008-07-06 20:08:50 (Show Source): You can put this solution on YOUR website!Hi, I dont know what Im doing wrong I need help please. Here is the question: One year ago you invested \$4300 into three accounts that earn 3.25%, 4%, and 5.75% annual interest. The interest you earned after one year is \$193. You remembered you invested three times as much in the 4% account than you did the 3.25% account. How much did you invest in each type of account? This is what i have so far, I dont think its right. x + y + Z = 4300 0.0325x + 0.0400Y + 0.0575z = 193 Y=3x ----------- x + y + z = 4300 325x + 400y + 575z = 1930000 3x - y + 0 = 0 ------------ Solve the system of equations by any method to get: x = 700 y = 2100 z = 1500 =========== Cheers, Stan H.
 Square-cubic-other-roots/147393: can you explain in a more simpiler way about just sqaure roots? 1 solutions Answer 107764 by stanbon(57984)   on 2008-07-06 19:55:32 (Show Source): You can put this solution on YOUR website!sqrt(8) Factor 8 into two factors where one of them is the highest perfect square that divides 8. -------- sqrt(8) = sqrt(4*2) = sqrt(4)*sqrt(2) = 2*sqrt(2) =============== Sqrt(27) = sqrt(9*3) = sqrt(9)*sqrt(3) = 3*sqrt(3) =============== Cheers, Stan H.
 Equations/147392: the equation y= -1777x+27,153 can be used to predict the number y of gun deaths in the united states x years after 2000, that is, x=0 corresponds to 2000, x=3 corresponds to 2003, x=4 corresponds to 2004, and so on. predicit the number of gun deaths in 2004 and 2007. in what year will the number of gun deaths be 11,160? 2004_____ 2007_____ the predicted number of gun deaths will be 11,160 in the year_____1 solutions Answer 107763 by stanbon(57984)   on 2008-07-06 19:51:57 (Show Source): You can put this solution on YOUR website!the equation g(x)= -1777x+27,153 can be used to predict the number y of gun deaths in the united states x years after 2000, that is, x=0 corresponds to 2000, x=3 corresponds to 2003, x=4 corresponds to 2004, and so on. Predict the number of gun deaths in 2004 and 2007. In what year will the number of gun deaths be 11,160? ----------------- 2004_ g(4) = -1777*4+27153 = 20045 ---------------- 2007_____ g(7) = -1777*7+27153 = 14714 ---------------- the predicted number of gun deaths will be 11,160 in the year_2009 11,160 = -1777x + 27153 1777x = 15993 x = 9 ============== Cheers, Stan H.
 Equations/147390: In 1992, the life expectancy of males in a certain country was 66.4 years. In 1996, it was 69.9 years. Let E represent the life expectancy in year t and let t represent the number of years since 1992.1 solutions Answer 107760 by stanbon(57984)   on 2008-07-06 19:40:16 (Show Source): You can put this solution on YOUR website!In 1992, the life expectancy of males in a certain country was 66.4 years. In 1996, it was 69.9 years. Let E represent the life expectancy in year t and let t represent the number of years since 1992. ---------- You have two points: (0,66.4) and (4,69.9) slope = (3.5)/(4) = 7/8 -------- intercept = (0,66.4) --------- EQUATION: E(t) = (7/8)t + 66.4 ============ Cheers, Stan H.
 Quadratic-relations-and-conic-sections/147388: please help me solve and graph 1 solutions Answer 107757 by stanbon(57984)   on 2008-07-06 19:34:05 (Show Source): You can put this solution on YOUR website!solve and graph 5x^2-9y^2-30x-18y=9 ================ Complete the square on the the x-terms and on the y-terms. ---------- 5(x^2-6x+9) - 9(y^2+2y+1) = 9 + 45 -9 (x-3)^2/9 - (y+1)^2/5 = 1 ---------------- This graphs as a hyperbola with center at (3,-1) ------- Comment: Since a hyperbola is not a function this cannot be graphed on this site. -------- Cheers, Stan H.
 Radicals/147366: radical 27/8 (the fraction is in the radical sign) and radical 15/6 (the fraction is in the radical sign)1 solutions Answer 107755 by stanbon(57984)   on 2008-07-06 19:25:53 (Show Source): You can put this solution on YOUR website!radical 27/8 -------- Multiply numerator and denominator by sqrt(2) to get: sqrt[54/16] = (1/4)sqrt(54) = (1/4)sqrt(9*6) = (3/4)sqrt(6) ================== Cheers, Stan H.
 Radicals/147368: Simplify: radical z/y8 (z/y to the 8th power is inside the radical sign)1 solutions Answer 107754 by stanbon(57984)   on 2008-07-06 19:14:37 (Show Source): You can put this solution on YOUR website!radical [z/y^8] (z/y to the 8th power) ------------- sqrt[z/y^8] = (1/y^4)sqrt(z) ============ Cheers, Stan H.
 Radicals/147369: radical 50/y4 (y to the 4th)1 solutions Answer 107753 by stanbon(57984)   on 2008-07-06 19:07:44 (Show Source): You can put this solution on YOUR website!radical [50/y^4] (y to the 4th) ---------- = sqrt[(25*2)/y^4] = (5/y^2)sqrt(2) ============== Cheers, Stan H.
 real-numbers/147374: Problem: To save the environment, the Lions Den Cafeteria sells an empty reusable 24-ounce plastic mug to students for \$2.99. Using the mug, a student can get a 24-ounce soft drink for a reduced price of 69 cents. (1) If a student buys the mug and uses it only once, then what is the cost for that one drink? 1 solutions Answer 107752 by stanbon(57984)   on 2008-07-06 19:05:06 (Show Source): You can put this solution on YOUR website!Problem: To save the environment, the Lions Den Cafeteria sells an empty reusable 24-ounce plastic mug to students for \$2.99. Using the mug, a student can get a 24-ounce soft drink for a reduced price of 69 cents. ----------------- (1) If a student buys the mug and uses it only once, then what is the cost for that one drink? --------- Paid for the mug: 2.99 Paid for the drink: 0.69 Total paid: 3.68 ---------------------- Cheers, Stan H.
 Travel_Word_Problems/147375: A fishing boat traveled 3 hours against a 6 km/hr current. The return trip took only 2 hours. Find the speed of the boat in still water.1 solutions Answer 107751 by stanbon(57984)   on 2008-07-06 19:02:01 (Show Source): You can put this solution on YOUR website!A fishing boat traveled 3 hours against a 6 km/hr current. The return trip took only 2 hours. Find the speed of the boat in still water. ------------ Against current DATA: Time = 3 hrs ; rate = b-6 : distance = tr = 3(b-6) = 3b-18 km ----------- With current DATA: Time = 2 hrs ; rate = b+6 ; distance = tr = 2(b+6) = 2b+12 km ----------- EQUATION: distance with = distance against 2b+12 = 3b-18 b = 30 kph (speed of the boat in quiet water) ============== Cheers, Stan H.
 Finance/147380: I need help. Please.......... Describe what the graph of interval [-4,10] looks like.1 solutions Answer 107749 by stanbon(57984)   on 2008-07-06 18:57:40 (Show Source): You can put this solution on YOUR website!Describe what the graph of interval [-4,10] looks like Draw a number line. Mark two points are -4 and 10 Put a solid dot at x = -4 and at x=10. Draw a solid line segment joining those two dots. The dots and the line segment are the graph of the interval [-4,10] -------------- Cheers, Stan H.
 absolute-value/147379: I'm attempting to help my child with an absolute value problem that she cannot solve and it has been a long time since I have had Algebra. Help please! Please show work with explanation and then I will work it through with her not providing the answer directly. Thanks! Find the absolute value inequality for the following: x < 6 or x > 111 solutions Answer 107746 by stanbon(57984)   on 2008-07-06 18:49:14 (Show Source): You can put this solution on YOUR website!I'm attempting to help my child with an absolute value problem that she cannot solve and it has been a long time since I have had Algebra. Help please! Please show work with explanation and then I will work it through with her not providing the answer directly. Thanks! Find the absolute value inequality for the following: x < 6 or x > 11 ------------------- Draw a number line; mark 6 and 11 on the line. Find the point half-way between 6 and 11: that is 8.5 or 8 1/2 -------------- x < 6 and x>11 are all the points that are more than 2.5 away from that middle point. ---------------- The Absolute Inequality must describe all the points that are more than 2.5 units from 8.5: |x-8.5| > 2.5 =============== Cheers, Stan H.
 test/146923: segment p1 p2 has length L and endpoints p1=(2,7)and p2=(8,3). find a point on p1 p2 that is 1/3L away from p1. A.(6,11/3) B.(4,5) C.(4,17/3) D.(11/3,17/3) E.n/a1 solutions Answer 107713 by stanbon(57984)   on 2008-07-06 12:35:26 (Show Source): You can put this solution on YOUR website!segment p1 p2 has length L and endpoints p1=(2,7)and p2=(8,3). find a point on p1 p2 that is 1/3L away from p1. ------------ Let the point be (x,y): EQUATION: distance from (2,7) to (8,3) = sqrt(4^2+6^2) = sqrt(52) --------- EQUATION: distance from (2,7) to (x,y) = (1/3)(sqrt(52)) (y-7)^2 + (x-2)^2 = 52/9 --------------------------- The solution is a circle of points. -------------------------- Cheers, Stan H.
 Equations/146911: 1. Name the property of real numbers illustrated below. Be specific with the naming (include "of addition" or "of multiplication," if applicable). (-8)(13) = (13)(-8) 2. Combine like terms: -3x2 + 2x  4x2  9 + 6x  2x2 + 8 3. Solve for x: 8x  11 = -11x + 18 4. Solve for x: -2(x  5) + 7 = x  8  5x 1 solutions Answer 107704 by stanbon(57984)   on 2008-07-06 11:42:08 (Show Source): You can put this solution on YOUR website!1. Name the property of real numbers illustrated below. Be specific with the naming (include "of addition" or "of multiplication," if applicable). (-8)(13) = (13)(-8) commutative; multiplication -------------------------- 2. Combine like terms: -3x2 + 2x  4x2  9 + 6x  2x2 + 8 -9x^2+8x-1 ------------- 3. Solve for x: 8x  11 = -11x + 18 19x = 29 x = 29/19 ------------------- 4. Solve for x: -2(x  5) + 7 = x  8  5x -2x+10+7 = -4x-8 2x = -25 x = -12 1/2 ================ Cheers, Stan H.
 Polynomials-and-rational-expressions/147329: This question is from textbook algebra I didn't solve this one. I didn't understand it, but it's transforming equations, 24x+5=12x+41. Please help me, thank you=)1 solutions Answer 107701 by stanbon(57984)   on 2008-07-06 11:24:15 (Show Source): You can put this solution on YOUR website!24x+5=12x+41 subtract 12x from both sides;subtract 5 from both sides 12x = 36 divide both sides by 12 x = 3 -------- Cheers, Stan H.
 Polynomials-and-rational-expressions/147328: This question is from textbook algebra Ok, with this particular question I did it again and again, but my answer just doesn't add up. This is Transforming equations...Again. The problem is 3(x-5)+7=16, and I got 3x=38 The way I solved it was this way: 3(x-5)+7=16 3x-15+7=16 3x-22=16 3x-22+22=16+22 which equals to 3x=38, but I have the feeling it's wrong. Please help me, thank you=)1 solutions Answer 107699 by stanbon(57984)   on 2008-07-06 11:17:31 (Show Source): You can put this solution on YOUR website!3(x-5)+7=16 3(x-5) = 9 x-5 = 3 x = 8 =========== Cheers, Stan H.
 Polynomials-and-rational-expressions/147325: This question is from textbook algebra It's Transforming Equations: Multiplication and division, the problem is 3x+2/2=7, I got x=11. Please help me, Thank You=)1 solutions Answer 107698 by stanbon(57984)   on 2008-07-06 11:13:07 (Show Source): You can put this solution on YOUR website!3x+2/2=7 ----------- (3x+2)/2 = 7 3x+2 = 14 3x = 12 x = 4 ---------- Cheers, Stan H.
 Polynomials-and-rational-expressions/147327: This question is from textbook algebra Again, Transforming equation: Multiplication and Division, 2/3x=24 I got x=77, on my paper it said I did a math error, I don't understand what I did wrong. Please help me, thank you=)1 solutions Answer 107697 by stanbon(57984)   on 2008-07-06 11:08:02 (Show Source): You can put this solution on YOUR website!2/3x=24 ------- When you don't use parentheses your problem can be interpreted two ways: -------- 1st Way: (2/3)x = 24 2x = 72 x = 36 ------------ 2nd Way: 2/(3x) = 24 1/(3x) = 12 3x = 1/12 x = 1/36 -------------- Cheers, Stan H.
 Polynomials-and-rational-expressions/147326: This question is from textbook algebra The problem is transforming equations, 3(x+5)=4x. I started doing the problem I got stuck in the middle of it, but I managed to get through it and got 3.4, I am wondering if I can get some help with it. Thank You=)1 solutions Answer 107696 by stanbon(57984)   on 2008-07-06 11:03:06 (Show Source): You can put this solution on YOUR website!3(x+5)=4x 3x + 15 = 4x x = 15 ========== Cheers, Stan H.